Differentiation matrices for Lagrange bases are particularly useful. See [1]}
Chapter 2 for a detailed derivation. We give a summary here to establish notation. We suppose that function values \(\rho _k\)  are given at distinct nodes \(\tau _k\)  (that is, \(\tau _k=\tau _i \Leftrightarrow i=k,\)  for \(0\le k\le n\) ). Then the barycentric weights \(\beta _k\)  are found once and for all from the partial fraction expansion
\(\frac{1}{w(\mathbf {z})}=\frac{1}{\prod _{k=0}^n (z-\tau _k)}=\sum _{k=0}^n \frac{\beta _k}{z-\tau _k},\) 
